The diagram shows a house built with dominoes. This house has four stories and uses 24 dominoes.Simon broke the World Record by building a domino house with 73 stories. How many dominoes did he use?

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Introduction

Mohammad Abdel-Hadi 10 Heaths GCSE Maths Investigation

DOMINO HOUSE

The question that we have been given to solve is:

The diagram shows a house built with dominoes. This house has four stories and uses 24 dominoes.

Simon broke the World Record by building a domino house with 73 stories. How many dominoes did he use?

Investigate

To summarise the question about Domino House it is asking you to find how many dominoes are used in n stories to then be able to find out how many dominoes are in 73 stories.

Method

There are many parts that I will want to include in my project to be able to find the answer and to also allow the reader to understand exactly what I'm doing step by step. I will also explain each section as I work through the investigation.

The sections that I will include in my project are to set out the project and make it simple to understand. Firstly I will use diagrams to make my project easy to understand. I will try to work systematically to make the project simple to understand.

Using the rule that I have just worked out I will now make predictions for a domino house with 5 stories and a domino house, which has 6 stories.

My rule is n(squared)+2n=d

When n=5 5(squared)+(2x5)=d

25+10=35

So a domino house with 5 stories will use 35 dominoes.

When n=6 6(squared)+(2x6)=d

36+12=48

So a domino house with 6 stories will use 48 dominoes.

I am now going to test these predictions by drawing a domino house with 5 stories and a domino house with 6 stories and then count how many dominoes are used to build these domino houses in order to see if my predictions are correct.

Here I can see that this domino house uses 35 dominoes, which means my predictions are correct.

The graph is not symmetrical. I will now choose another set of dimensions (8x4) still for the ratio 2:1 and see if I spot a pattern. x x 4 8-2x x 4-2x 8 If I now swap the dimensions for this rectangle with the equation I used before I get V=x(8-2x)(4-2x).

As the value of "b" increases, each wave's period of this function compresses horizontally along the x-axis. It can be easily observed that varying values of "b" do not change the amplitude of the graphs as the graphs in Figure #4 have the same amplitude.

Doubling all inputs doubles outputs and doubles cost, and so on. A second disadvantage is that linear programming may also yield a non-integer solution and therefore may give unrealistic results or outcomes to the problem. However, it is sometimes possible for two special cases to arise when we attempt to solve linear programming.

we have derived the formula: The root can be found by keep on using this Xn+1 formula, until a small difference between the last Xn and the new Xn can be observed, maybe only the sixth decimal place onward (going onto seventh decimal place, eighth decimal place and so on)